Generalized sequential preventive maintenance policy of a system subject to shocks

The paper proposes and analyses a generalized sequential preventive maintenance policy of a system subject to shocks. The shocks arrive according to a non-homogeneous Poisson process {N i (t); t S 0 }, whose intensity function r i (t) varies with the number of maintenance actions (i - 1 ) that have already been carried out, and the time (t) that has elapsed since the last maintenance action. Upon the arrival of the k th shock, the system is maintained or repaired minimally with probability θ i , k and q i , k respectively depending on the number of maintenance actions (i - 1 ) that have already occurred and the ordinal number of the arriving shock (the k th ) since the last maintenance. In addition, a planned maintenance is carried out as soon as T i time units have elapsed since the (i - 1 ) th maintenance action. If i = N, the system is replaced rather than maintained. The objective is to determine the optimal plan (in terms of N and T i ) that minimizes the expected cost per unit of time. It is shown that under certain reasonable assumptions, a sequential preventive maintenance policy has unique solutions. Various special cases are considered.